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Math Help - Hyperplane, any clear explaination?

  1. #1
    Newbie ibrex77's Avatar
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    Hyperplane, any clear explaination?

    Hi math guys,

    I am happy to join you in this forum (I also like the fractal symbol) . My math background is not that good , that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols.
    I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

    Best regards,
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ibrex77 View Post
    Hi math guys,

    I am happy to join you in this forum (I also like the fractal symbol) . My math background is not that good , that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols.
    I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

    Best regards,
    In a nutshell:

    In \mathbb{R}^2, a hyperplane is a line of the form ax+by=c (note that this is the standard form of a line).

    In \mathbb{R}^3, a hyperplane is our ordinary plane of the form ax+by+cz=d (note that this is the standard form of a plane).

    Now, hyperplanes (in general) are planes in \mathbb{R}^n. They are of the form \sum_{i=1}^n a_ix_i=b\implies a_1x_1+a_2x_2+\ldots+a_nx_n=b.

    Unfortunately, there is no real way to visualize these things in 4 or more dimensions!

    Does this little bit make sense?
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  3. #3
    Newbie ibrex77's Avatar
    Joined
    May 2010
    From
    Amman, Jordan
    Posts
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    Thanks

    This is just what I am looking for. using line and plane which are somethings I already know to define the hyperplane is really a great idea .

    Thank you again .
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